After a good deal of messing around, I have a workable, networked solution for scanning with my HP2840 from a 64-bit Windows 7 machine:

1. Install XP Mode on the 64-bit machine

2. Either at Setup, or after installation, set the Network Adaptor on the Virtual machine to be the Network card on your 64-bit machine, not the default Shared Networking (NAT). To do this after installation, click on Start -> All Programs -> Windows Virtual PC -> Windows XP Mode. Make sure it is not running full screen, so you can see the Menu bar. Click on Tools -> Settings -> Networking and select your Ethernet card from the dropdown box.

3. Use the Windows XP CD that came with your printer to install the printer. Mine did not find the printer automatically - I had to specify the IP where it is located (so you need to make sure that your printer's IP is fixed - but that's a good idea anyway, so you can have a bookmark to it in your browser)

4. You should now have the printer installed within the Virtual machine. HP Director should be available within the Virtual machine through Start -> All Programs -> HP -> HP Director.

6. To avoid death by a thousand clicks, right click on the HP Director program icon and pin it to the Start menu, Toolbar, or wherever to like to have things.

This does work. To describe it as clunky, however, would flatter it considerably. Like others contributing to this and related threads, I am a long-standing IT user, at least semi-professional, and I am not impressed with HP's customer support on this one. Any laser printer should outlive two or three computers, and that means two or three operating systems - it is simply not good enough to fail to provide a proper, native solution for an obvious use. Next time I need to buy a printer (or advise my multi-thousand-computer employers what to buy), I'll be suggesting a good look at Brother. And Microsoft's documentation for XP Mode isn't exactly brilliant, either: I had to find out how to connect the Virtual machine to my host machine's network from an independent forum, despite Microsoft's trumpeting of the capacity to do exactly that in one of their glossy brochures about XP Mode.

Working fine. It was a pain to work out what to do and to set it up, but having set it up, it's no trouble to use. The only issues are:

(i) It takes a long time to load. But that's all right - I just leave it running once I've loaded it.

(ii) The list of drives that you get when you are saving the scanned documents will look a bit unfamiliar, because they have the names/designations that the virtual machine assigns them, not those the host machine normally gives them. This could be offputting for a naive or very occasional user.